Dot more layout control

[steveroush]

1. Attribute declarations are not additive, they replace earlier definitions. You want style=“rounded,dashed”

2. To try to keep nodes in the sequence you want, use something like this (invisible edges):
   { rank = same; C3R1 -> C3R2 -> C3R3 -> C3R4 [style=invis] };

3. The underlying problem with the last rank (column) is a bug in dot related to rankdir=LR (setting rankdir causes odd node ordering (#1953) · Issues · graphviz / graphviz · GitLab)
   Here is your graph tweaked. Correct w/ std rankdir, funky result w/ rankdir=LR:

    digraph G {
    //	rankdir="LR";
    	boxme [shape="box"]
   
    	start -> C1R1 ;
    	start -> C1R2 ;
    	C1R1 -> boxme ;
    	C1R1 -> C2R1 ;
    	boxme -> C2R2 ;
    	boxme -> C2R3 ;
    	subgraph cluster_0 {
    		graph [label= "surrounded"; color=blue; style="rounded,dashed" ] 
    		node [ style=filled, color=green ];
    		{ rank = same;  C3R1 -> C3R2 -> C3R3 -> C3R4  [style=invis]} 
    	}
    	C2R1 -> C3R1 ;
    	C2R1 -> C3R2 ;
    	C2R2 -> C3R3 ;
    	C2R2 -> C3R4 ;
    	C2R3 -> C3R5 ;
    	C2R3 -> C3R6 ;
    	{ rank = same; C1R1 -> C1R2   [style=invis] }
    	{ rank = same; C2R1 -> C2R2 -> C2R3  [style=invis]  }
    	{ rank = same; C3R5 -> C3R6  [style=invis] }
    }